



\subsubsection{Tests of proportion}
% Intro
% This far, the Mann-Whitney Wilcoxon's test were used for the metrics' hypothesis
% testing. 
To give more confidence to our observations, tests of proportion were also
conducted considering counted defects.
% Scenarios
The tests verified the proportion of counted bugs on two scenarios. The first
scenario verified the overall proportion of counted bugs {\it by technique}.
The second scenario verified the proportion of counted bugs by each technique
{\it per use case}.

% Resultados
The null hypothesis is that the proportion of counted bugs for each
scenario is equal. 
% Primeiro cenário
For the first scenario, the
test result, {\it p-value} of approximately 0.515,
could not reject the test null hypothesis and it is possible 
that the proportion of detected bugs per technique is equal.  
% Segundo cenário
With the same confidence level of 95\%, we verified that
the proportion of bugs detected per use case is greater on TaRGeT.
First, we rejected our null hypotheses with {\it p-value}
of 0.006, and then we checked which technique had a greater proportion.
 
Thus, in the pairwise comparison, the proportion of bugs detected by TaRGeT was
better, while on general they are equal. These results increase the confidence
of our previous observations, as discussed on Figure~\ref{fig:bugs}-A and
Figure~\ref{fig:bugs}-B.




\subsubsection{Analysis of correlation}



With the purpose of measuring how experience and use cases'
complexity influence the time and detected bugs output, the
Spearman's correlation between the experiment factors was analyzed. 

Hence, a Spearman's correlation analysis between dependent variables (time
and number of detected bugs)
and independent variables (experience of the participants and use case's
complexity) was conducted. 

\begin{table}[!t]
\caption{Analysis of correlation}
\label{tbl:result-correlation-general}
\centering
\begin{tabular}{c|c|c}
\hline
\bfseries & 
\bfseries Experience & 
\bfseries Complexity \\
\hline\hline
\bfseries Bugs & 0.14 & 0.45 \\
\hline
\bfseries Time & -0.10 & 0.69 \\
\hline
\end{tabular}
\end{table}

The correlation indexes varies from -1 to 1, where a -1 value indicates that the
variables are inversely proportional, a value near 0 indicates that they are not
correlated, and a value near 1 indicates that they are positively correlated.


% \begin{table}
% \caption{Analysis of correlation}
% \label{tbl:result-correlation-general}
% \centering
% \begin{tabular}{c|c|c}
% \hline
% \bfseries & 
% \bfseries Experience & 
% \bfseries Complexity \\
% \hline\hline
% \bfseries Bugs & 0.14 & 0.45 \\
% \hline
% \bfseries Time & -0.10 & 0.69 \\
% \hline
% \end{tabular}
% \end{table}


Table~\ref{tbl:result-correlation-general} presents the general correlation
analysis between the experiment variables. There is
a {\it weak correlation} among the experience and quantity of bugs, 
as well as among the experience and time. 
On the other hand, there is a {\it
moderate correlation} between bugs and UC's complexities, and a {\it strong correlation}
between time and complexity.
These correlation indexes are stronger or weaker for each
approach, as presented in Table~\ref{tbl:result-correlation-tech}.
For the ad hoc technique, the greatest difference is in the complexity column,
where the bugs correlation index increased and the time index decreased. For the
TaRGeT technique, these indexes were inverted, the bugs correlation index
decreased and the time index increased.



From the correlation analysis, it is possible to state that the more complex a
use case is, more time an participant tends to spent modeling and testing it.
Also, the more complex a use case is, more susceptible to have defects it is.

